{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Linear Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/ageron/handson-ml2/blob/master/04_training_linear_models.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures. We also check that Python 3.5 or later is installed (although Python 2.x may work, it is deprecated so we strongly recommend you use Python 3 instead), as well as Scikit-Learn ≥0.20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)\n",
    "\n",
    "# Ignore useless warnings (see SciPy issue #5998)\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", message=\"^internal gelsd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually corresponds to the following code, with a legend and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"linear_model_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1  # learning rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "\n",
    "def plot_gradient_descent(theta, eta, theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "        theta = theta - eta * gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch == 0 and i < 20:                    # not shown in the book\n",
    "            y_predict = X_new_b.dot(theta)           # not shown\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(X_new, y_predict, style)        # not shown\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 # not shown\n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 # not shown\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     # not shown\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           # not shown\n",
    "plt.axis([0, 2, 0, 15])                              # not shown\n",
    "save_fig(\"sgd_plot\")                                 # not shown\n",
    "plt.show()                                           # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "             eta0=0.1, fit_intercept=True, l1_ratio=0.15,\n",
       "             learning_rate='invscaling', loss='squared_loss', max_iter=1000,\n",
       "             n_iter_no_change=5, penalty=None, power_t=0.25, random_state=42,\n",
       "             shuffle=True, tol=0.001, validation_fraction=0.1, verbose=0,\n",
       "             warm_start=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.24365286]), array([2.8250878]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25214635],\n",
       "       [2.7896408 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)   # not shown in the book\n",
    "    plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)              # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         # not shown in the book\n",
    "save_fig(\"underfitting_learning_curves_plot\")   # not shown\n",
    "plt.show()                                      # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           # not shown\n",
    "save_fig(\"learning_curves_plot\")  # not shown\n",
    "plt.show()                        # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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SwamIcqVdu3Z06tSJAQMG5Owui4uL49dffyUyMpJ777232H0XRGHl2C233MLFF1/MhRdeiMvlYvbs2cyePZupU6eqf09VQEQq1REVFSUFERsbW+B7lYnZs2dLeHi4+Pr6SufOnWXHjh0yY8YMCQwMlIkTJzre386dOwXI99i5c2dOvZiYGLnqqqvEz89PGjVqJE8++aRkZGQ4No6q8v0pngBrpALIjoKOs8kUkapzX1ZEubJ3714ZMGCANG7cWPz8/OT888+XO++8U7Zs2eL4eLIpjBwbPXq0tGnTRvz9/cXPz086d+4s77///jnbrir3SkXh+R+flw/XfyjprnSP8pLKFCMl8PsoD7p06SJr1qzJ971NmzbRtm3bMh6R4hT6/VVNjDFrRaRLeY+jIM4mU0DvS6Xw6L3iHEdPHaX+5PoE1Qji+OPHPXyrSipTHLfZGWM+NMYcNMYcN8b8aYwp0BPNGDPcGHPIGJNkjHnPGFPT6fEoilK5UZmiKNWPmCMxAETWj3Tcobw0FitfAMJFJBi4ARhvjMnjuWaM6QM8DvQEwoEWwDOlMB5FUSo3KlMUpZoRE2cVn3b127kLR4+G994rcduOKz4iEiMiqdkvs46W+VS9F3g3q34i8Bww0OnxKIpSuVGZoijVj41HNgLQvkF7W3DkCEycCA+WfJdXqbinG2PeMMacAjYDB4EF+VRrB6zP9Xo90NAYk2cbgTFmsDFmjTFmTVxcXGkMWVGUCozKFEWpXuSx+Pj5wZtvwuOPl7jtUlF8ROTvQC3gCmAukJpPtSAgKdfr7Oe18mlvuoh0EZEu9evXd3q4iqJUcFSmKEr1QURyfHzaNchSfIKDYcgQeKbkq9elFpBARFwishxoBuRnm0oGcgeAyX5+orTGpChK5UVliqJUD5LTkmlcqzH1A+rTtJazUZuhFBWfXPiQ/3p8DNAx1+uOwGERiS+DMSmKUnlRmaIoVZhaNWux4cENHBxx0O7o+vlnmDwZduxwpH1HFR9jTANjzO3GmCBjjHfWLos7gKX5VH8fuN8YE2mMqQs8CcxwcjyKolRuVKYoSvUlJyP7e+/ByJEwa5Yj7Tpt8RGsCXofkAi8BPxLROYZY8KMMcnGmDAAEVkETAK+B3ZnHU87PB5FUSo3KlMUpZpxIvWEZw65/v3h9tvhllscad/RXF0iEgfkm+lNRPZgnQ9zl00Bpjg5BkVRqg4qUxSl+tF3Vl9i4mL49q5v6dq0K/Ttaw+H0GxriqIoiqJUCESEmLgYjp0+RrPgZqXShyo+Ctu2bWPIkCF07NgRb29voqOj860XGxtLz549CQgIoEmTJowdOxaXy1XseoqiVF0KK1cUJTcHkw9y7PQx6vrVpVHNEBgzBlavBgfzijq61KVUTmJiYliwYAGXXnopaWlp+dZJTEykV69eREZGMm/ePLZv386IESPIzMxk/PjxRa6nKErVpjByRVHOJHf8HvP99/D88/C//0FMjGN9qOKj0K9fP2688UYA+vfvz9GjR/PUeeutt0hJSWHu3LkEBwfTu3dvjh8/zrhx4xg5ciTBwcFFqqcoStWmMHJFUc7kj8N/ANC+fnto3hwefhhat3a0D13qqqAkJCQwZMgQQkNDqVevHqNGjQKge/fuTJs2zdG+vLzOfRssXLiQPn36eCgut99+OykpKfzwww9FrqcoStlT0eSKopzJukPrAOjcuDNERMDUqVb5cRC1+FRAjh07xmWXXUZQUBDvvfceGzduZMyYMYSHh7N9+3YGDRrkUV9ECuVD4+NT/K978+bNXH311R5lYWFhBAQEsHnzZvr161ekeoqilC0VUa4oypmsO5hL8SklqodKbow9ctOvny2bP99dNn26LRs82F124IAta9LE8/yoKFu+dq27bNw4WzZuXImGO2HCBA4dOsSiRYu44YYbeOKJJwgNDWX06NE8+uij+Pn5edSfOXMmvr6+5zxKQmJiInXq1MlTXrduXRITE4tcT1EqPSpXSixXFOVMZtw4g9f6vkbH2T/AokWQkeF4H6qqVzBEhJkzZzJo0CBCQ0NzymvXrk1SUhJDhw7Nc06/fv1YvXp1qY/NnCnkseM9s7yw9ZTKz8qVsGwZREdDt27lPRqlICqyXFEUgMxMiIuDS5pdQmZMWyY/Nolo17N029semjm7rb16KD75bYPLPSPLZvBgz1kZ2BlZfufnnpFlM25ciWdlW7ZsIS4ujt69e3uUu1wuhg0bRmBgYJ5z6tWrR+3atUvU77moW7cux44dy1OelJTkYeEpbD2l8rNyJfTsCWlpUKMGLFlSzZQflSuK4hgffQT33AMNGkD80VpI5rPU8B7Lkr016OZwOJ/qsdRVidi5cycAzZs3zylbsWIFu3btolOnTvmeUxYm6YiICDZv3uxRtnfvXk6ePElERESR6ymVn2XLrNLjctnHZcvKe0RKQVRUuaIo2Xz0EQyYNoXmV39Dhgtc4kUaNUpFrlQPi08lwtvbJmVLSEgArIl65MiROc/zoyxM0n379mXy5MmcOHGCWrVqATB79mz8/f258sori1xPqfxER1tLT7bFR+PTVVwqqlxRFICjR20C9vOum0FMQCBePr0g07vU5IoqPhWMqKgo/Pz8GDlyJGPGjGH27NkkJCTQunVrPvnkEzp06EB4eLjHOSEhIYSEhBS7z1OnTrFgwQIA9u/fz/Hjx5kzZw4A1157LQEBAQwdOpSpU6dy8803M2rUKHbs2MG4ceN45JFHPLauF7aeUjk506dnyRL18akMVFS5oigrV8KkSXBR11SWx8cyMCGTC3t+xadH+zJlWo3SkSsiUqmOqKgoKYjY2NgC36tMzJ49W8LDw8XX11c6d+4sO3bskBkzZkhgYKBMnDjR8f527twp2CzYeY6dO3fm1IuJiZGrrrpK/Pz8pFGjRvLkk09KRkZGnvYKW+9Mqsr3V1VZsULE31/E29s+rlhRuPOANVIBZEdBx9lkikjVuS8rqlypSlSVe6WsyJYpIOJbI0PMfZfKgbq+IiAPXrCkwPNKKlPU4lMBue2227jttts8ys4//3zuvffeUukvPDy8QHN3biIjI1m6dKlj9ZTKRX4+PWrlqTxUVLmiVF+yZQqAK8NgdkWzYIDhnv3NeP+baKZmQGmEiVLnZkVRCkW2T4+3t/r0KIpScqKjwcsrKySWTwaZLZaRfNdf8f3iUxo29mLr1tLpVy0+iqIUCvXpURTFSbp1g44dbWaKVY0fYFvgKjo3ngRAp06wfj20bet8v6r4KIpSaLp1U4VHURRncLngzz/h66+FheN3E/9nA6IeOA+wCtH69XD77c736+hSlzGmpjHmXWPMbmPMCWPMb8aYvgXUHWiMcRljknMd0U6OR1GUyo3KFEWpumzaZAMWNgjJ5N75e3hk3hEC/tgEWIvP77+XTr9OW3x8gL3AlcAe4FrgU2NMBxHZlU/9lSLS3ckBSAVJjZCcDCdOQK1aEBRU3qOp+KgTpFIA5S5ToGLIFZUpFRuVYUVn1Sq49FKsk8+bb8Knn8Jf/gK4LT6lgaOKj4icBMblKvrKGLMTiAJ2OdlXfvj6+pKSklLu8SGSk635LjPTOm61aaOC6lykpKRoFFglD+UtU6BiyBWVKRUflWFFZ9Uqu3S+bM+PtL6sA02vuSbnvbAwSEmBI0esVchJSnVXlzGmIdAGiCmgykXGmKPGmD+NMU8ZY0qkiDVo0ID9+/dz6tSpctW+T5ywAgrs44kT5TaUCo+IcOrUKfbv308Dp+9upcpR1jIFKoZcUZlScVEZVnxWroQuF2fQ7+N+NHulGYeTD+e8Z0zpWX1KzbnZGOMLzAJmisjmfKr8CLQHdgPtgNlABvBCPm0NBgYDhIWFFdhndmTgAwcOkJ6eXrIPUAJSUyE+3uYgNMbGIcgnb6eSha+vLw0bNtTIzspZKQ+ZAhVDrqhMqdioDCs6x47B7t0Q9p+/8ewfyXzWN4yGQQ096mQrPmfk1i0xpaL4GGO8gA+ANOAf+dURkR25Xm4wxjwLPEY+QkpEpgPTAbp06XLWKVdwcHCFuPlyh/YvIAegoiiFpDxlClQMuaIyRalKrF4N3TueIGTmJwxPhQN3dsxTJywM9u1zvm/HFR9jPQDfBRoC14pIYadIApS/V7JD6LZfRXEGlSkWlSlKVWLlSujYvRZjb7oa17ff0PLSa/PUCQ0tnaWu0vDxeRNoC/QTkZSCKhlj+mat12OMiQCeAuaVwngURancqExRlCpGtmPzR76bmNwdLj/v8jx1QkJs5nancTqOT3NgCNAJOJQrlsadxpiwrOfZC+o9gT+MMSeBBcBc4Hknx6MoSuVGZYqiVD1E4PdVpwlrv489SXsIrhlMZP3IPPVCQqxvm9M4vZ19N2c3LQflqvso8KiT/SuKUrVQmaIoVY/tm9L45XhbvEaEU7e9N91ad8fbyztPvdDQSqD4KIqiKIqinI09n67iysy9eG8LYPcn8cSnJuZbr7SWulTxURRFURSlzPgmpQcxj2zn4VsPUcu/NrX8a+dbr04dG7wzI8OGcHCKUg1gqCiKoiiKkpt16+C86IZkXtz1rPW8vKBuXUhIcLZ/VXwURVEURSl9UlORVb+wbh2s85lGg8kNeGvNW2c9pTSWu1TxURRFURSl9HnnHUy3S3kxdTir4r4jPiWe2jXzX+bKpjQcnFXxURRFURSl9ElNJcMvkCMRF/Pj7h8B6NWi11lPKY0t7YVSfIwxbxljxBjTJJ/3LjDGpBljXnV2aIqiKIqiVBkeeYRJD+5i87X1SHWlclGji6gfWP+sp5TnUtfKrMeL83nvFeA4MM6JASmKoiiKUjX5aVMoxxt9C0DvFufOPlqeS12rsh49FB9jzHVAX2CsiOS/Eb+Ks3IlvPCCfayu6DVQFOfQ35NegyrH+PGwYAGSKaxZK/x++gsArm9z/TlPLY2lrkLtjBeRLcaYBHIpPsYYX2AKsBF429lhVQ5WroSePSEtDWrUgCVLql8SQb0GiuIc+nvSa1Dl2LABxo4Fb28Or9iBKySRPSd20jCwIZedd9k5Tw8NhS1bnB1SUZybVwFdsjIlAwwD2gD/EhGXs8OqHCxbZn+cLpd9XLasvEdU9ug1UBTn0N+TXoMqR0QETJoEo0bx68Hz6Nq8A78N+Y3p/abnm6biTMrN4pPFKuBa4IIs689TwP9EZImzQ6o8REfbGUn2zCQ6urxHVPboNVAU59Dfk16DKoevLzxqU+itGwdRnQ2dGnWiU6NOhTq9vBWf3A7OPYCawAhnh1O56NbNmmGXLbM/zupojtVrYFm5Uq+BUnL096TXIDeVWq4kJVmlJyAgp+jX1cKgB86WczgvoaHO7+oqiuLzC5AJ3A90ByaLyA5nh1P56NatEt6QDlPdr4H6JOTl8GFYvBiWLy/vkVQ+qvvvCfQaQBWQK//6l9XaZs2Cyy5DBH7MfJEjh+bjv20s17S6plDNlFscHwAROQHEYq09R4AJzg5FUSon6pMAJ0/CwoUwYgRceKFd1p8zBzp0KO+RKUrlpFLLlVOn4I8/4OBBq7kA+/ZBasvPWHtkJemu9EI3Va8eJCZCZqZzwytqvtNfgfbA6CxFSFGqPdXRJ8HlgjVr4LvvrGVnzRqIioLevWH6dOjSxZ1N+aGHynesilIZqdRyJSAAVq2C1avhggsA+PynjWTU/43gmsH0bnnu+D3Z+PhArVpw7JhVgpyg0IpP1vb1aGANMNOZ7hWl8lMdfBJEYPt2q+h89x18/z00bWoVnZEjoUcPCAoq71EqStWh0ssVX1+4zL1d/aNN74IPDGg/AD8fvyI1lb3cVeaKD/AocD5wp4iIM90rStWgKvokHD0KS5e6rTppadCrF9x8M7z+OjRuXN4jVJSqTaWTK3PnWk1t0iTwcys3qRmp/C4fAHB/5/uL3Gy2g3Pr1s4M86w+PsaYesaYO4wxLwDPAVNEZNVZ6tc0xrxrjNltjDlhjPnNGNP3LPWHG2MOGWOSjDHvGWNqFv+jKIpSElJSrJIzahR07gwtW8IHH1g/na+/tmv0M2fCXXeVndKjMkVRKgkpKfDggzBtGnz6qcdb/9s8j3TfeNqFdCSqcVSRm3bawflcFp8+wEdYZ+ZXgMetCbjdAAAgAElEQVQL0d5e4EpgDzbuz6fGmA4isit3RWNMn6z2rgYOAF8AzxSiD0VRHCAzE377zVpzvvsOfvnFOib36gVTp8Ill1hrdTmjMkVRKgP+/naGNHMm3H23x1v/+WUWAEO63o87BnLhKVPFR0Q+Bj4ubGMichLPZKVfGWN2AlHArjOq3wu8KyIxAMaY54BZqJBSlFJj506r6CxebP0HGjSwis6wYXDllRAcXN4j9ERliqKcmz//hLfegvnz7cYDLy+7Ff7hh6F9+zIcSJcu9jiDuwNmkbjnM+688MZiNet0LJ+i7uoqEsaYhti0FjH5vN0OmJfr9XqgoTEmREQ8dDtjzGBgMEBYWFgpjVZRqh6JiZ5+OsnJVtHp2xdefhmaNSvvERYNlSmK4ubUKfj7320oifvug88/t5sMTp+Gzz6zmw8uvxz++1+7M6pU+OILO4O6/PICq2xcF8QtLe+jnn/xunDa4lOUXF1FImsX2CxgpohszqdKEJCU63X28zxfj4hMF5EuItKlfv36zg9WUaoIqal2x9WYMXDxxdC8ObzzDrRpY/0ODx6EDz+EgQMrpdKjMkVRsti1y+oaGRnWkvvii3apukULiIyEp5+2derVs/V27y6FQWzeDHfeCVddBRs35nn7eOpxkk4nsXp1voagQlPWPj7FwhjjBXwApAH/KKBaMpDbsJ79XOMDKUohycy08ibbovPzz9C2rZ3pTZpkd4TUrALuvSpTFMXNtm02hMTIkXaZuiC3mZo14e234d//trLgp5/spgXHaNUKhgyxQXbatcvz9pSVU3hl1Sukpkyja9d7it1NhV/qysre/i7QELhWRAoK0RgDdASy3b87AofPNEkriuLJvn1uRWfxYuuX06sXDBoEH30EdeuW9widRWWKoriJi7NL1U8/bXWOc2EMDB9ud5f362fjCjrmy+fjA6+8YmdgZ2hfyWnJTP1lKsdTj3N+YPMSyaXKsNT1JtAW6CciKWep9z5wvzEm0hhTF3gSmFEK41GUSk1SEsybB//4h00F0akTLFpkrcu//AJbt8Kbb9r4OlVN6clCZYqiYHeM33AD3HZb4ZSe3Dz4oA2EOGCAdYAuNunpMHGiHUw2XnlVielrp5N4OpFwr8voE9GjBB1ai0+FXeoyxjQHhgCpwKFc29aGAD9hc31FisgeEVlkjJkEfA/4A58DTzs5HkWpjKSlWYUm26qzYQNceqm16nz0kVV88pEz5UqaK42t8VuJjYslNi6WmLgYYuNieahryfJVqExRFDfDh1u/vfHji3f+q69Cnz7w3HMwblwJBvH66zaL6v/+l2+VhJQEnv/peQAabRtNj2uKvoU9N/XqVWDFR0R2A2f7hB5B7UVkCjDFyTEoSmVDBGJj3YpO9jp8797w7LPWMdG/gN0QK1eWbUj71IxUtiZsxdfLlwtCbQ6eJTuWcM2sa8jIzMhTf/3h9SXqT2WKoljmz4dvvoH16wv26TkXvr42KOlFF8FNN9lJ1JmcU6b8/e9WUD3xRIH9PP3908SnxBPdPJoNr11H92IqatkEBtodbE5RqtvZFUXJn4MH3YEDFy+2Toi9e8M998CMGda0ey5WrrSxOrKTGC5Z4qzysyluE78f+t3DgrMtYRsucXFfp/t478b3AGhepzmuTBct6ragXf12RNaPJLJ+JO3qtyMiNIK3edu5QSlKNeTwYRg82G5RL6l/TtOmdqXqvvvg1189g5QWSqZERtodFT75qw8bDm/gzTVv4mW8+FfEqwwLNJx3XsnGHBgIJ0+WrI3cqOKjKGVAcjL88INb2TlwwPro9O5tnRSLs9Ni2TIroFwu+7hsWdEVn5T0FLbEbyHmiFVsRl8xmqAa1ogy/JvhfLP9G4/6XsaLVvVaERrg1sxa1G1B8hPJBPgGFP1DKIpyToYMgb/9Dbp3d6a9gQNh9myrAD35pLs8X5nSJR0eeMA6Ed6YFYCwAKUHrIy4uOnFdG7cmbiNFzoy5mzlLD3dmWjyqvgoSimQkQGrV7sVnd9+g65drZ/Of/9rc2F5e5esj+hoOyvLnp1FR5/7nP3H9/Par68Re9T64uxI3EGmZOa8f1PETXRt2hWAq8+/Gn9f/xwrTrv67WgT0gZ/X891Ny/jpUpPEdi6FdauhR077G6Vu+6yM1pFyY8vv7ThcmbPdq5NY+A//7FLXQMG2Ng/UIBMmT0b3n8fFiyw5qCgoLO0DO0atOPnv/1MqiuVIffDFVc4M+Zsq0+dOiVvSxUfRXEAEfuH9t139li2zDoh9upll8KvuML5P7du3awpOvd6/Mm0k2w6usnDybhd/Xa82OtFAFJdqbz484s5bXgbbyJCI+zyVGikhyVn5OUjnR1wNUfE5kCbMMF+Xy1awJo1dsb997/bxwqQG02pQJw8Cf/8J7z7rvPxuM47Dx55BEaMsMGXIX+ZwqV3wqZN1inoLErP4eTDNAhsgDEGYwx+Pn789JONNeQEAQHWz0cVH0UpR44cccfSWbzY/rH17m23mr79NjRsWHp9J6clU9O7Jt26+dKtG4xbNo4Br85k17FdeeoeSj6U8zy8TjjjrhxHRGgE7Rq0o3W91tT0qQIRDis4p09bn4otW+yOvfPPd7+3bZsNVXDbbfDJJ1Uj4KTiDOPHw2WXWUNLaTBihHXZWbzYTtLAKjvdgjZkhXava81DEyactZ3ktGR6zOhB63qt+eD/PqCuf13277ehONq2dWasAQHO+fmo4qMoheTUKbvjKtuqs3u3TezZuzeMGmXTQhR3t0VBHE89zqa4TTnWm2wn4z1Je/jlgV+4uOnFgLX07Dq2K2e3VbYFp12DdrRv4M5S6GW8eDpad3iXNWPGWD+vn3/Ou0OvVSu7nHHHHTZGyxdfWCGvVG/+/NMuR23YUHp9+PnZnH3/+hf8/nuW687ChXDLLVYDWrjQrnmdhTRXGn+d81f+jP+Tmt418fPxA6wydeWVzoXecHJnlyo+ilIALhesW+feefXrr3YbaO/eNmDgxRef1cevSCSdTiI2LpZUVyrR4dEA7E3aS9i/80+gWcO7BvuO78tRfP5x8T+4v/P9tKzbEl9vXS+pSPz4I3z8MfzxR8FhCWrUsK4Ud95pHVk/+KBsx6hUPEaOtEfjxqXbz003wWuvwfTpdsmVCy+0GU3Dw21E5rOQkZnBnXPvZMHWBYQGhPLZrZ/l+ADOn28VeadQi4+ilBLbt7sdkr//3gqdXr2sSbhHD2cyHMfGxbJ8z/IcP5zYuFj2n9gPQOfGnVk7eC0ATYObEuIfQtPgph4OxpH1I2lZryU+Xu6fb/M6zUs+MMVxkpPtDpq33z53iAIfH3jvPZvM8YMP4O67y2SISgXk+++tovzJJ6XflzEw7ZGdXP23cO66yxDctKk1/5xD4zqdcZr7v7yfObFzCK4ZzDd3fZMT2+v0aStD33zTuXGqxUdRHCI+HpYudVt1UlKsRefGG60japMmxWz3VLyHYjM4ajDtGtgkfjN/n8mkFZM86vv5+NE2tC2dG3XOKfMyXhx57AhepoKFaVYKzdix1tzfr1/h6gcG2j+7Xr1stO7WrUt3fErFw+WyTscTJ9qlqFJnyhQiH3+cZy95l4kT77buPOdQehJTEunzYR9WH1hNgG8ACwYsoHNjt+xatgw6dID69Z0bplp8FKWYnD5t/SyyrTpbt9odV7162SzHkZHF89NJSU/hse8ey1F0Dp887PH+hQ0vzFF8ejTvwcHkg7QNbUu7Bu1oV78d4XXC8fbKu79dlZ7KS3y8DV0QE1O08zp2tArT3XfDihUVLz2JUrp88IH9k+/fv4w6rFcP0tO5o8NGwt+CoUM5Z8DB2n61aRTUiPA64Xzx1y/o1MgzBPSXXxZe2S8savFRlEKSmWlDvGcrOitXQvv21qrzyitwySXn9N1DRIg7FWcdjI+4HYx9vX357u7vAGuxmbl+JslpyQAE+gbStn7bnOWpS5tdmtPedW2u47o215XaZ1YqBm+8YWO+Fcdq+NBDNi/bjBk2cF115uhRu/KSkmLjY0VGls5GgopASgo89RR8PNvF/hMH2Xd8H0dPHSUhJYGTaSdJc6VxwwU3cH5duy0w5kgM2xO3U8+/Hg0CG9AwsCHBNYMxZ7s4Bw7Y7YVXXWVf33svXHghtTp3Zmhd64j//vuep7gyXXy7/Vsa12pMp0ad8DJefPB/H5CRmUFIQIhHXRHr3/Ptt05eGfd2didQxUepcuze7V66WrLETmh697aOe599BrVr53+eiHD45GH8ffyp7Wcrvb3mbcYsHUN8St4MeX4+frgyXXh7eWOM4Y1r3yAkIIR29dtxXu3z1FpTjUlJsQ6jy5YV73wvL5g2Da6/3ipPTsQuqUykpdkdTR99ZHc1de5sQ8h4e1vflxMn7LV57DFo1668R1sykk4nkZCSwPl1z2faNLigxx9cvaQL6d+l51s/sn5kjuLz4R8fesTlAgiqEcR5wefRoWEHZvd3Rz384/AfND6YTOjlvTEBAXbbWN2s7eqd7TLV44/DBRfYjRyRnZJZuXclS3cuZdaGWew9vpdLml7CivtX4GW8cmTkmfz+u12ii4hw4uq4cTJthSo+SqXn2DHrp5Nt1UlKsnEv/vIXmDQJws7YGCUiHEw+mGPBiY2LJfaofZ54OpHp109nUNQgAAJ8A4hPiSe4ZrDHFvHsZarcys3dHdUbVbHMnGmtiSWJYdKli10uGDcO/v1vx4ZW4fniC7ubqVUra/2Ijs7r63LggLWG9expd11Pm5YVdqYS4Mp0sXLfShZuXcg3279h3cF19G3dlw+u+ZrJk+HbZS2JmpNBw8CGnFf7POoH1CckIIRA30BqetckvE54TlsXhF7Ada2vIz4lniMnj3DwxEGS05LZdHQTNbyzTNnp6YiPD5e8cwmn00/zU31DcrDw73eioXFjAmsE8mCXB+nVohe1akHv0dO5Yu54Mhbt94jq3qJuC26KuImMzAx32/nw5Zd2N5fTFjm1+CjVmtRUWLXKHU8nNtYG+erd21p0LrzQzphFhP0n9vPt9lgOJR/ino735LTR9vW2HE89nqft2jVr5yxXAdwYcSP7hu+jSa0mZzcfK0oWmZk2Nsp//1vytp5/3i7tDB3q/Ay6opGaCg8/bLf/v/66nbgURJMmNiL68OEwebI1WLzyik2/UFF/pusOruM/a//DF5u/8PAB9PXyRUR4/nkbPueidoGcuuBUTjycszGw00AGdhqY81pESDydyN6kvaRmnLbrVu+9R/Kvy4kIjWBv0l563xXPad8UOPUHbP8DgBvauPedX9bN8P7Xe/ESb7o26UqP5j24tvW1RIdHn9OKnZFh7/vPPivixSkEavFRqhUiNhlw9vLV8uX2T6BXL3jxRTvj8/ODP+P/5Ks/v2La/JicXFTZyk1N75oM6DAAHy8fjDF0D+vO8dTj1nKTvVW8QTsaBzX2UHCCawYTXLOE6ZCrApmZ1jPcz8/tbbt3rz3CwtzT7QMHYN48u52jzLwzKxYrVtjoy5dfXvK26teHRx+1zs6fflry9ioqhw7ZJb2GDW2Ou8KGjfD3t9fm+uutM3i20uRUfC0n+X7n97y19i0Azq9zPjdecCN9WvWhR/MexB0IoPM/rZwDCqX05IcB6vnXo55/PVsQ8wIcOkStBYv5bchvAJxKP8Xh5MMcOXmE+JR4UtJTiGoSldPGre1uoW5iTx55oBmLN9QoUjb4L76woqBr12IN/6wEBFjrviOISKU6oqKiRKn67NsnMmOGyJ13ijRsKNKihcjgIS5586NdMnvtApn882S573/3yRebvsg558P1Hwrj8DhCJobIFe9dIUPnD5Wk00nl+IlKgcxMkVOnRJKT3WUZGSIrV4r88INn3XnzRKZMEdm1y1327bci99wjMnOmu2zPHpELLxTp3dvz/IgIERDZtMld9thjtmziRHfZjz/asssvzykC1kgFkB0FHU7LlIceEhk/3rn2kpNFGjcWWbfOuTYrEocOiVxwgchTT4m4XMVv5/hxkWuuscfx486Nrzj8uu9XuX3O7fL8j8/nlB08cVBGfjtS1h1YJ5mZmR71777bfv4SMW2aSOvWIhs2uMvWrxdZtapYzd1/v8iQIUU7p1s3kc8/L1Z35+TNN93jKalMqYB6sVIdOXHCOoJ+9x18t1iIO2K4+mpr1fHtN4yY4yuZFRfL9D9Pwp/u82rVqMVNETcB0LVpV/7e5e+0a2AtOJH1I2kQ2ICVK23bMSFZSfdKm7Q0uxgdFOSeeu7ZY9Nxh4W5UyEfOmSDtoSEeEare/hhmwjsnXfcU9/sKf/48W5Lyuefw6232qny55/bMpfLfkgfH0jP5Rz5xhvwzTfWVNY8K9jh1q12+0ZAANzjXgbkjz+gaVPPz+Tvb609qanusvPPt8Fmcicla9bMrstU0wA0GRnWzP/zz861GRgIo0fbW2D+fOfarQjExVk/nTvugKdLmEmlVi3rX/LQQ3D11VaWlJZTeLZMyUnkiTUiLNq2iBd/fpEfd/8IwM/BPzOq+yi8jBeNghoxsffEPG2tX293QG3dWsRB7N0LjRq5M9tu2mQb+egju0YKdt2/mLz8so3FkzuP19lYtcqKtBtvLHaXZ8VJHx9HZ07AP4A1QCow4yz1BgIuIDnXEV2YPtTiUzVISxP54acM+ee4bRJx0zypcfUL0ujBu6XpM1ESPKGupKan59S9/N3Lcyw4DSc3lKtmXCX/+Pof8vqvr8vvB38/az8rVoj4+4t4e2eKv3+mrPgm11QwM9NaRr75xvOkefNEXnxR5M8/3WVLl4rccYeddmRz6JC1hFxyief5nTpZq8fate6ysWNt2dNPu8vWrLFlnTt7nt+kiS3ft89dNnSoLXvjDXfZ11+L1Kwpcsstnp/p0ktFrrzSWn+yeeMNkWHDRDZudJdt2iTy3/+K/PKLuywtTeS330S2bvUc0xkz1KJACWZnlU2mfPONSNeuJW8n3ZUue47tkc1xm2X9ofXy5+Hdcl54qqxcWfK2KwrJyfbWHz26RLdXHjIzRf75T/uzTCoFI69bptjHn3/OlHmb50mX6V1y5FTwC8Ey8tuRsvvY7nO216ePNdYUibvusvJg0SJ3WWyslQm5ZGdJWbRIpHnzwlnQbrtN5N//dqzrPMyZI3LzzfZ5SWSKlILF5wAwHugDFJCVJoeVItLd4f6VCogr08X2hB3s2eVL7Ipwu818z0JSbrgZP9dpglqB+MEhH0AgLA6O/O99mrW/DCIimHD1BGomHKfDwrUEBjeBewe7G//HP2D/fptoJjtM6LPP2i0fTz/NsgP3kpYGLpchLSWdZQ9/TrctA209Y+zU0OWyVprsmdOMGXaxunVrt+Vi1y6bcKlGDWvRAGtV2bzZbgnNTe3aEBzsaXFp0cLmvMgdGaxxY2vdaX5Guol//9uaDnJPV8eMgX/+0zMozLXXWr+b3Bhjp6Nn8uCDecsiIvJ6zPr6QqdOeeuWn8dopZIpH39srRdFxZXpIj4lngaBDQC79ThqepRnpYEQ/WUzrt3dlSeueIIuTbqUfMDlhIjNVt++vU387eTtZYz9CT30EPTta60pgYHOtb9sGVkyxT6+M3cb/61lzRwNAhvwaLdHGdJlSKF8Axcvhm3bYPDgs1R6+21YtMju78/Oe3L++dYEsnOnu17bts6lQs+iTx973H03zJlTsO/UDz/Y6/LOO45270GFtfhkH1hBda7Z2fLitK0WnzIgPV0kLk7kyBHP8iVLRL780tOSMG+eyLPP5qwrb43fKj+8P1429YiU9wZcJGHPdxSvsTUl+HFkW1Cw7KsTKR9/LPJ97HphHPJreA0RkH9P7i9vr3lblu9eLiefzbKOjBzp7icmxpZFRHiOqWVLW57bOjN8uC176SX37MzLJf6clBVXjPQ8/y9/scepU+6yGTOs/8rvuaxJ27eLzJrlaR3JyLAWlJ07C7yUK1aIPP+8fayu4ICPT2WQKadPi9StK7J/f+HPOZV2SiYtnySNXmok13x4TU55SnqKNJvSTFpPbS2Rr0dK45cai/cz3jkWhRV73DfU6v2rZePhjfk1X2F57jlrkUlJKb0+XC6Re+8Vue46R40gsmKFiJ+/y8Pic+2sa+WVla/IybSThW4nI8O6082Zk6vgf/8TmTDB0wTWs6eVZ598ktP/80+dkhXfn3buQ52F1FRrlRo4MH8frF27RBo1si6DpcmyZSJXXGGfl1SmlKficxI4ivXYeArwKUzb1VrxOXZMZO9ezz/pXbtEvvrKOrFlEx9vvStfecXz/H/+00qBvXvdZRMmiDRtKvL66+6ypUvtrdGjh+f5QUEiIGnxcbIpbpPMiZkjf/S60Nb94ANJThZp91J3ua0/IiCzI91OxuETmtp6fn4iYk35iSmJIv36iYSGejrjfvqpSK9eIm+95S6LixMZMULk5Zc9xzR/vpUcuW3ahw6JbNuWY58tL+XjTJN4dVV+ylDxKVeZMm+eXWEsDJmZmfL+7+9Lk5eb5PxGLph2gaRmpBZ4ToYrQ556dZN0uud9OZXmlgHRM6KFccgl/7lEPtnwiaS7HPyXLwUWLrQipygKYnFJS7N/2oMGObOctufYHrlr7l3iO6iHPPpUfPF/0wkJsmzge/JSqzfd48rMtJoziOzOtUQ2b57Iu++KHDhQbjIlOdmuoA8eLJKQ4FneqVNesVwarF4tkv1TrayKTwvgfMAL6ADEAqPPUn8wdp1/TVhYmLNXs6Skpdlf8Jm/4m+/tX/Ip3Np5fPmiTz5pPXtyObnn0Wuv95aTbI5fVqkWTPr65GbXr3sV5bbJ+XVV23ZP/7h/oP//IAtO/Nadehgy3MrSU88Ycuee85d9uuv9gd43XUiYn/s474fJ6suaSrftw+S0NE+OcL61v7IwiuHyP2d10lQkEjYwKek+/Ar5ZWH+sncGU/Kqr2r7G6qzEzrN5Lbb6WK8/zzVkCBfXz++XOfUxUpI8Wn3GXK4MF55xr5kXQ6SQZ8PiDnN3TRWxfJwq0L8+z0yY+UFCsWsnd4ZbgyZOj8oRL8QnBOe81faS6v/fKanE4vuUXA6UnDwYN2h9qyZc60VxhOnLB/mLlFXFFJTk2Wp5Y+JX7j/YRxSI3nasisP2YVfELu7/KXX+x2pFwTuRMbdtpJZEgjz/NGjRJ5/HHPyWkuylOmxMdbq0+9etZd8LbbROrUsR/NSR+tgoiJcRv8K6Xik0/924G1halb6NlZfLxdnjhxwl22a5fI3Ln2jz2bY8fsPsIz958OG2a39OZeQpk0yVoncm/f/eUXexnP9Ghs2NCWHzzoLrv/flv29tvusnnzbFmWkiEi9i6yy+CetsUBA6zUyG1T/Oorkb59ZcWIOblmApmy4p437fbl3Hz3nV2qOnbM4zqd3rFVNu74RT7Z8ImMXTpW+n/aX8b/4L4eGw5vyLNNPGB0uPjcc52E3vGo/O2RnbJggeeuakUtPtmUheKTT33nZcpZyMy084zcu/3z41jKMWk1tZUwDgmcECjvrntXXJlF28M9ZYrbyTObk2kn5c3Vb0rrqa1zfqPNpjSTn/f8XMRP4sbp+9flsqvKTz5ZsnaKw8GD9vuZPbto52VmZsqH6z+Upi83zbmuf/3sr7Izcae9IJ98YteCshk5UiQkROSjj9xln31mZXm/fjlFTzzukuUt7rb/O7ldB85BRZApu3eLjBkj8s47nn9vpc2uXe65fFVRfP4KrCtM3ajgYKsVZ5OZaRcYg4M9lYR+/ezH+9//3GX/+Y8t+9vf3GWHD9uy0FDPq3zxxbY89501frwtGz3aXRYTY/u/5hrP8++9V+T//s/TT+bLL0WeecbT4nPwoFV+cpeJ2LvryJFCq9KFmQmcTj8tGS73j2zs0rES8VqEh+9A9tHjv3aZ68gRkQ8/TpUOj4yUkKtnSuiFq2XAwGT58MOyvekrK+rjU26KT+FligOKT2ysFcqF+blO+HGCXPjmhbI5bnOx+jp5UqRBA88Netm4Ml0yJ2aOdHijg9R+obYcPXm0WH2IOG9dePllG+fFSX+bovD77yL1658jrM2hQyLff59zcR/79jFpPgxZ1BL5tktdWb57ubtuWJi9ONu2uctGjLBluS/W7t3WMv/TTyJilePQ0OIv9VVXmXLkiNUpRSqY4oONBO0HvAB8kPU8zzo70BdomPU8AtgIPF2YPqJA5OqrPa+Iv7/9KLlNDoMH2314X33lLluyROTGGz33Dqak2C3GZ9qof/rJLiklJrrLkpKsopTbx6aC4DkTyJQZ87fIrD9myROLn5CbPrlJ2kxrI17PeMmGw+7gVg9+9aAwDjHjjLSa2kpu+PgGeXTRaBk56wO5d+R6uegiq09ef7393cbGlo1JU6lalERIlYlMcUDxmTLFipzCcjZfnsIwYYLd0VwQrkyXh2J1Ov203D7ndlm1t/DB7Jy0LsTG2j+t7duL30axcblEFiwQ+eADmT/fGs137RI7ge7cOUchERGRqVPtf8nf/y4iIpvjNkuXsY1FQDIbNPBsd9Aga3rLrfgcPmxnhAVEYszMtH9fpbntu6py8qS9D0UqnuIzDpAzjnFAGDauRlhWvZeAw1nOiDuAZwHfwvQR1bp13hCmhw7Z5Ztq9q98Mu2krDuwLkeYrVgh8siTcWIeuCyPBYdxiNczXjJ/y/yc87cc3SJr9v0my385JS+8YDcPBAXZoLtPPy2yfLl1YVKUklBCxaf0ZYoDis9f/mJX0fNjX9I+6Tmzp2yL35Z/hWJw7Jj1tSisIvHqqldz5MBdc++SfUmF87VzwrqQnm4N6Ln3TxQLl8tToVi1ys7IVq92ly1fLtKqlcitt7rLMjNFfH3t311KikyZYt0d027+qy2bZX11MlwZMv/VhyQmIkQyJ03KOT3t9Ck7gXYgdPasWdYZuLysXpUZl0vEGPtYUsXHiNubYRYAACAASURBVBUalYYuXbrImjVrynsYZc6Wo1v4df+vxMTFEBNnM4rvTNyJIFwRdgU/3mcjhaa50qj9Ym2a127uziKelYvqgtAL8PPxY+dOd4LPpUuhQQOb4LN3b7jySoqUm0VRzoUxZq2IVNigMyWVKadO2eDV+/bZEE4e76Wf4soZV7LmwBpuiriJL/76RQlH62bMGIiPh7feOnfd46nHeeGnF3hl1SukulIJ9A1kzBVjGN5teLHzQhWWiRNt0PDFi91p3nLIzLTRwP2zQjQlJdl4NSLw2GPuepdfDr/8YpNZZceeevxx2/iECTZjKcCvv8Ill0BUFOT+Tu+4A7y94bXXkNp1GDoUvDfHMG3iKbwjWvNT0gYeXvgw6w+vB+C7u7+jV4tChCsuAgkJNm7R3Lk24LlSdAIDbVD7oKCSyRRVfCoQyWnJbIrbRGxcLDFxMQyJGkLLei0BeHjBw7y2+jWP+j5ePrQJacNlzS7jPzf8J6c83ZWOr7dvzuuEBKvgLF5slZ2TJ20I8uwjO7+kUvXIL7R+WVPVFZ+FC22y3B9+8CwXEe6ceycfb/yY8DrhrB60mtCA0BKO1k1cHFxwAWzYkDfDSEHsSNzBo98+yhebrQLWsm5L3rjuDf7S8iyp0ItDRgb4+LB5M3TvDhtf/IpGe36F226z//4AM2fCAw/YSIbTp9uyI0esFlmvntXqsrniCpud+KefbIMAX31lA/tdfz1cc40tS0mx6WEaNjxrvor0dBvcsFm7vaT1GMXHGz8GIKx2GFP+MoWb297skazYCW6/3Q7r1VcdbbbMKU+ZUr8+xMRAw4Ylkymaq6scOZF6gmd+eIbYOJtJfHfSbo/3L2p0UY7i06N5D46cOuJhwWkd0poa3jXytJuZ4cvSH9yKzpYtdsLUu7eNZtq+fXkG4lXKipUrbR6ktDQbcHrJkvJTfqoyixa5/3dz8/769/l448cE1Qhi/h3zHVV6wP4J3HsvvPQSvPJK4c5pUbcFc/86lyU7ljBs0TBi4mI4cvJI8QYQF2eTh/n5wYABuTppAbt2kZmYxKBBtRg7Fhot+wRmzYKWLd2KT+3aVkE6ftx9bmgo/OtfNgeViFtQffmlne7XyCXvrr/eHrnx97fa4Dnw9YXoJ15m7PdjkY2n8PPxY9Tloxh5+UgCfAOKdz3Owscf25xc69Y53nSZUt4yJTDQmejNqviUIkmnk3KUmmwrTq2atfjs1s8A8PPxY+ovU0nPtKkNanjX4IKQC2hb3yo3HRp2yGnr1na3cmu7W/PtJzPTzvq++84qOytWQGSkVXReesnemDXy6kdKFefM0PrLlqniUxosXmyNF7nZd3wfwxYNA+C1vq/RvkH7Uun7scesHvH44565Ys9FzxY9+W3Ib3wW+xl3tHfn2Ji/ZT5XnG5Anf3xdj2mXj37xrvvwuTJcP/97iWoffvs6w4dPBWfLGXlk1cPk5FRi4ceAprcZBWiDm6ZlpNypWZNd5mXV/5a3JlpYZzAJwXxOYX/jluZ2GsSD0eHO98HNqPOsGGwYIF7Ra+yUt4yJSDArliUFFV8HCAxJZEa3jUIrGETwrz+6+u8sPwF9p/Yn6duHb861rnKGHy9fZnadyoNAxvStn5bWtVrhY9X4b6SvXvdFp0lS+zkqVcvGDLEJvwurazESuUhOtoqvNmzs+jo8h5R1ePoUfv/nzu9mYhw/5f3k5SaRL82/bin4z2l1n+TJnDnnTaT9qRJ56icng7JyTlKhG+6iwGv/QDxc2HOHHYk7qD/Z/1Z/N9MrtiRQfrCr/G95lp7bmqqNR1v2+Zur3lzuOeevBaWVavYf7IOw7r6smyZda2hf3975KaMZ2NLdy4lISWB/pF2HCO6jaBH8x7USepB797Qoh5cd52zfZ4+bT/2sGHQpcIu9hae8pYpavEpBxJSEqzl5ojbwTg2LpaDyQf58P8+5M4L7wSs783+E/vx8/EjIjSCyPqROctT7eq382hzaJehheo7Kclq19lOyQkJ1uTYuze88ELePJeK0q2bVYrL28enKrN8ub2uZyZvvKHNDWyK28T0ftMd9xU5k1Gj4MILrSGmfn3gjz+sI3BUFHTubCt98421sFxzDXz9tS2rWRPef9/+O584QUZmBpefdzk/NfmeFODdhYO45bxXuDXyVkz//jbJbliYu+N69fKaugAJrc9Dg2xe3Hbt8rxd5qw9sJYnv3+SRdsWERoQyl9a/oXgmsH4+/rTo3kPwK7YXX89fPSRnUA6gYidiDZrBqNHO9NmeVPeMsWpRKWq+OTD0VNHiY2LJe5kHLdE3gLY7MlNXm5Cqis1T31/H38SUhJyXveP7E/PFj05v875eHt5F2sMaWlWdmVbdTZssDdZr17WotOxYz47JBTlDLp1U4WnNPnxR6sP5MYYw0MXP8QDnR+gpk/N/E8sDunp1vk3tyfziBE0W7WKh655nylTWvLCC1iHkhdfhGeecSs+DRvaf+LTp3MP1DoV16kDvr60qdWGJfcs4ctLvuSfi0exJX4Ln875K5MaT+K5q56jb/u+hRrm3LnWODR7tnMfvTj8fuh3nv3h2RxH7lo1ajH80uH4evnmqXvxxfD553DLLVaX61u4j3pWXnrJ6qDLl1ctWV2eMiUwUJe6HGFr/Fa+3f6ttd4ctdacuFNxAATXDM7x7vf28iaqSRRprrQcy03b0La0a9CO8DrheBn3nR0SEEJIQEiRxiFivdUXL7bHTz9Bq1bWovPcc9Y52a90d50qilJEfvoJpkxxv05zpeVsOCi20nPwoN0iVqeO22s6Pt4qL7VqQWKiu+5vv8GKFTw8dBtt/9WS4cOhweWXw8CBnutvHTpYpef/27v3+KjqM4/jn4ckAgaQW4iooCJgaCpBbhYpCywg2K2A0lVUVLSWatdaLct6WazXarWu1bbWllVLlUqr1NvqbqtVUm9BLgIiWFNRucj9fhGJJL/94zchIU5CMjkzc07m+3698iIzczLnycnMwzO/a83upYsuOuSmmTGuYBz/0vNfeHTxo9xcfDOL1i9ixjszOLPH4auBHTvg6qv9h7PmAdZ8DbF933YufvZiXih9AfAfTL8/8PtMGzytzgHmQ4bAc8/B2Wf7unHy5MRjuO8+ePBBXxjn5ib+PHIotfjUk3OOTXs3+fVvNvnuqbN7nX1w+mbxJ8Vc9X9XHfIzrY5odbCo2Xdg38FR/m9e9magsa1bV1Xo/PWvPlGMGuW7zWfO9BMcRCScdu+G99+HAQP87VU7VjHokUFMO30a13ztmvhdXAcO+I//lU0As2fDnDl+SnflDKWFC/26M6NHVxU+7dv7rF/5kbfyf9Pbb4cDB+jUpw+TFsKdd8L998eZ7ZSVFRtsUz/ZzbKZ0m8Kk3pP4qEFDzHqpFEHH5u3dh6lW0s5r/C8LxV3113nTz1kSL1PFYjyivKDrettW7Rl9c7VtMxuyRX9r2Da6dPo3LpzvZ5n0CDfjXPmmf5ve/vtDRuK5Jz/mVmzfNFTvWdQGk+Dmw/j2j9fy8L1C1mxecUh3VDg3xiVhc/AYwdyaZ9Lq8bgdCqkS5suSemX373bf5Cr7L5avx6GD/fFzo9+5Gd6apq5SDSUlPiepMqW2BtfvZH1e9azYM08rN0HsHGjXxG00siRPgEsW1a1CN/y5b5vqLCwqljp1QvOOefQ/gQz3+qTU6ObZvDgg9/eeKOfzfnDHwb3H+6ROUcy9fSph9w3/dXpvPLxK0x7eRpT+k7h0lMvpVu7bhQX++FD770XzLnr4+PtHzNzyUweWfwIcy+ZS48OPTAzHhv/GJ1bd6ZTbqcGP2dBgR9mcPnl/k8wa5b/kxzOhg1+XNPHH/ui5+ijE/iFpE4ZPbj5012fHjK4ePnm5azdtZZPfvDJwYKleFUxSzYsAeCo5kdVdU/l9WLYCcMOPlfR0UU8Ou7RpMR54AAsWFA1IHnxYt+XPGqUb9Hp27dBH8JEJERefx3Gn7IS7n2Gda1h9obZHJF1BHf3ux669/LdUjt3Vn2aadbMJ4XVq6sKn3/9Vz8fvfqUn+7d/YCTmmoWPTXk58MVV8Btt8HDDwf0S9bgnOOCUy5g82ebeXfju9zx+h3c8fod/FOX4bz/1ER+9stzaNs2uU3V63av47m/P8cT7z3BG6vfOHj/Uyue4sYhfgXnoqOLGnWOTp18t9d//7dfL/Gss3xrVrwCaNs2v0TRHXf4Yimd3XxNXca2+CzZsITjfhZ/qeE1u9bQ9Sj/UeeuEXeRZVkUdiqkc6vOSZ9ZAb6Zs7S0aj2d4mI44QT/QW/6dN/8e2Twa2OJSDKUlfnpWpXdUr/9rf8f7sorYcIEXnsN7hvxd5g2je1FnXFnOyYXTaZLtz5+9kF+vl9JuPJN/9hjfj+Y6kmgqMh/BWTaNOjRA669NjkzqsyMy069jEv7XMprq17j4cUPM2fFHF5bMxe+Npftx5QBfujA9n3byT0iN+4iq4ka/4fxPPfBcwdvt8xuyfiC8UzpN4Whxw+t4ycbzgymTPG16YMP+sa7jh39h9cuXfxQq1WrfOvOmDF+nZ5+/QINQWrI2Baf8opy2rdsT2Fe4cEWnMK8Qgo7FZKfW7WC15jucZZSTYJNm/z0vspixznfonPuufCb3zRsUTERSYOyMt9vVb1radQomDvXL7dbWUF88ol/sw8cyP5vTmDRIjj5173Z9elk7t3yGM2sGdd9/Tr/P+aSJV8+Twr6Ptq2hZtu8uvGvPxy8rrOzYyhJwxl6AlDubDdLzjvlmcYcMlTTOg14eAx01+dziOLH6Fv576c0ukUeuX14sS2J3JM62PoelRX8lv55FheUc7WfVvZ+flONu3dxLrd6/hw24eUbitl8frFvHTRSwe7rHKPyKVFdgvOOOkMzik4h3N6nUPr5q2T80vGtGvnP7hef73vxnv7bd+tdfLJfkbf449r3bRUOfLIQ8f2JypyhU/vo3uzZNqSerfgBL2vyGef+Sbuyu6rVav8c48c6ZtCe/Y8fLIJw/5JIhKzbJkvdHbvrnrz5uT4JdFXr64qfM4/32+AWVTE737nG2+W7ejCrLFHMnNhBRd+9UK6teuWll+hek658ko/S/3ZZ/0MpWTatQu+d1lbHr//UsaOvfSQxzbu3cj+8v2UrC2hZG3JIY+dXXA2T5/3NAArt6/k5F/Wvs3EwnUL+UYPv5Di3SPvZsY3ZxxcLDaVsrP9RLnqk+UktXJz/UrYjRW5wienWU6Dip7G7itSXg6LFlUNSF6wAE491efJhx7yzZ41Fy9LdkwiEqAWLfwYm927fTUDfhBemzaHriFRUAAFBZSUwFVX+eE6I0Y4ul1TBs3hhq+nZ5W6eDnlgQf8eJMxY5K7TcI11/hzjx375cfmnDuH7fu2s2j9IlZsXsH7m99n9a7VrN+9ni5tuhw8rkV2Czoe2ZFWR7QiPzef/Fb5dG/XnZ4delLYqZB+nav6j45rox2VM1nGjvFpiET2FXEOVq6sKnTmzvXLwo8cCf/+775ps3W1ltWGtt6ke6+TKFHLmKREYaF/oVXXqfbZQMXFfi1BgLIy44JWMzhj8ncp7BTMoJogcsoNN/jxJnfe6adXJ8Of/uRbvxcvrv2Ydi3bMbLbSEZ2q3055K5HdWXztM1JiPDLlFOiLWPH+DREffcV2br10HE6+/f7TzHjxsEvfuELn3gSab1J914nUaGWMQmrYcN8j1izZv61OXy40f+YYDZiCjKnPPCAb50eO7ZqraGglJb6LrUXXoBWrYJ97mRRTok+tfjUQ237inz+uV9GvLJV58MPfUvOyJF+NkSvXvUbFJhI60269zqJCrWMSVj16OG7j779gw0MHVrBoEG1fDJKQJA55dhj4ec/94szv/NOcDNK9+zxywzdfrvv6o8K5ZToU4tPPQ0a5McjLl3qdy9++WWYN8+v4D5qFNx/v388kY2CE2290f5Jh6eWMQmr+fP9+/eDr1zCL+e9zFNdnjq4p19jBZ1TJk7069Fcf70vghqrosKPHRo40E/1jhLllOgLZYuPmV0FTAZOAWY75ybXcey1wHVAS+BPwJXOuS/vAJqgVauquq5eeQU6dPCFzlVX+RXijzqq8edQ603y6NoKhCunVJo/H7qf9g9+s/IlWmS3YPiJwwN77mS87h980I/d7tu3cftPOQdTp/qJbq+8Er1V5pVToi+sLT7rgDuA0fjkE5eZjQauB/459jPPALfG7kvIjh1+IHJlsbNjh++6Gj0afvpTv+BUMqj1Jnl0bYU05pTavP02tDhrBmyG8796Pu1btg/0+YN+3bdv7xfXGzrU58ERIxJ7nttvh1df9YVDMmeKJZNySrSFssXHOfc0gJn1B+qad3gJ8Ihzbnns+NuB39OAJLV/vx+sVjlOZ8UKv23NqFHw3e/6rqzKBVdFJJpSmVPqFw+8vaCcnOGzAJjSLxr9PQUF8OSTfhXiF19s2GDnigq49VZ44gk/NrJdu+TFKVKXsLb41Fch8Fy120uBfDPr4JzbWvNgM5sCTAFo166AM8+EN9/0b+aRI+EnP4HTT9f+KPJlmr6aMRLOKV0bsKPnypWQ3f1VNu3bQPf23Tnt2NMaGXbqDB3q9/D6xjf8bNWJEw//M3v2wMUX+5WKX39dK9FXUl5Jj1C2+DRAK2BntduV37cGvpSknHMzgBkAeXn93eWX+y1z2gfbwixNjKavZpSEc0r//v1dfU/y9tvQ8mu+tWfSKZNSsgdgkMaO9a3k48b598eNN8YvZioq/Do9//mffpPO2bP1wbKS8kr6RL3w2QO0qXa78vvdh/vB44+HCcFMoJAmTtNXM0rCOaUhFiyAvI7N2EhzLux9YZBPnTJFRX6A9q23+qU7Jk7074tu3fwWFPPn+5lgZr5l6IwzojeQOZmUV9InJweysnxh3hjpGgWzHKi+JXERsDFek7RIoiqnr2ZlafpqBkhJTlm0CO4e9Fu2/McWurfvHuRTp1SnTn621/Ll0LmzH/w8dSrce69f5+zHP/ZF3ujRKnpqUl5JryDWowp6Ont27DmzgCwzawEccM4dqHHoY8BMM/s9sB6YDswMMhZpuKbWb63pq9EXppxSUeE3Xe/bF1odEZHlig+jc2e/m3syKa9IkHJzYefOwx9Xl6C7uqYDN1e7PQm41cweBVYAX3HOrXbO/dnM7gHmUrXmxs1ferYIi9qbvan2W2v6auSFJqcsWr6D3KK3yW0zHEhgxdNGilpOAeUVCV7oWnycc7cAt9Ty8CEfkZxz9wH3BXn+sIjim1391hJGYcopj771PBtHXcK3njyL589/PlmniSuKOQWUVyR4ubmNfw6tdJME8d7sYad+a5G6/XXNMwCMPml0ys8dxZwCyisSvNC1+IgXxT1h1G8tUrvPvviMj5r9BYBxBeNSfv4o5hRQXpHgBdHio8InCaL6Zle/tUh8f/nwJSqy9tGn0wCOa1PXAtLJEdWcAsorEqypU/1aVI2hwidJ9GYXaTpmLXwWgHO/enbaYlBOEYExYxr/HBrjIyJShwMVB3hp1f8AcHav9BU+IhIMtfiIiNRhzc415HzRno7N8ijoWJDucESkkdTiIyJShxPbnUi/klIeKHoz3aGISABU+IiI1ME5WPyOMXRAh3SHIiIBUFeXiEgtdu3fRekne8jKOoZjjkl3NCISBLX4iIjU4qnlTzHgD8fSfPz3tVmnSBOhwkdEpBZ/WekXLTy5Q680RyIiQVHhIyISR3lFOX/9yK+U9o2eqd+mQkSSQ4VPxJWUwF13+X9FJDgL1i1g++fbydl9EqMHnpTucFJGOUWaOg1ujrCo7tgsEgV//vDPALh/jKFnzzQHkyLKKZIJ1OITYVHdsVkkCl5a+RIAJxwYTXaGfERUTpFMoMInwip3bM7KitaOzSJh9/mBz3ln/TsYzTj92KHpDidllFMkE2TI55imKco7NouEWYvsFmyatolJU99lYFGbdIeTMsopkgkCb/Exs/Zm9oyZ7TWzVWZ2QS3H3WJmX5jZnmpf3YKOp6kbNAhuuEEJSpqudOWUNs3bsGH+1+nTJ/HYo0g5RZq6ZLT4PAiUAflAH+BFM1vqnFse59g/OucmJSEGEWk6Up5TnHOUlxvLl0Pv3o19NhEJk0BbfMwsF5gA3OSc2+OcewN4HrgoyPOISGZIR07ZW7aXrvd3ZexjEzm6cwWtWyfrTCKSDkF3dfUEyp1zpdXuWwoU1nL8WWa2zcyWm9mVtT2pmU0xs4VmtnDz5s1Bxisi4ZbynFKytoS1u9by/qZ/0KdI8z9Empqg39WtgJ017tsJxPvM9CTQC8gDvgP8yMzOj/ekzrkZzrn+zrn+eXl5QcYrIuGW8pzyt0/+BkDenmEZN75HJBMEXfjsAWpOgWgD7K55oHNuhXNunXOu3Dn3FvAA8K2A4xGRaEt5TileVQxA+UdDKSpqcLwiEnJBFz6lQLaZ9ah2XxEQbxBiTQ7Q/sciUl1Kc8pnX3zG/E/nYxifvjVEhY9IExRo4eOc2ws8DdxmZrlmNhgYBzxe81gzG2dm7cwbCFwNPBdkPCISbanOKfM/nU9ZeRmFHYvYv7MdXbsG8VuISJgkY+Te94CWwCZgNnClc265mQ0xsz3VjpsIfIhvsn4MuNs597skxCMi0ZaynFKyxu/M2S17ML17g6kNWqTJCXwdH+fcNmB8nPtfxw9UrLwdd9ChiEh1qcwpY08eS3azbD5+8zSOVzeXSJOkLStERGIKOxVS2KmQi38DQzNniy6RjKJFKkREali6FA1sFmmi1OIjIgLM/Xgub6x+gzHdzqK0tA+FtS2RKCKRpsJHRASYs2IOv1r4K7ZsyuHEE/vQsmW6IxKRZIh8V1dJCdx1l/9XRCRRJWt9EtmxcDQ5OcopIk1VpFt8SkpgxAgoK4MjjoBXXoFBg9IdlYhEzd6yvby78V2arR3MEzP7UF7uc4tyikjTE+kWn+JiX/SUl/t/i4vTHZGIRNGCdQsod+XkbzmPAwcM55RTRJqqSBc+w4b5lp6sLP/vsGHpjkhEomje2nkAfG3wfkA5RaQpi3RX16BBvim6uNgnKDVJi0gi5n86H4BhA/KZ2xamTYPhw5VTRJqiSBc+4BOTkpOINMZxbY6jW7tuNN8ygAED4MYb0x2RiCRLpLu6RESC8PMzf87Kq1ey9YMCLVwo0sSp8BERiVm6FPr0SXcUIpJMKnxEJKPtL9/Pls+2ALBkibaqEGnqVPiISEZbu2steT/NY9Y7c1izBk4+Od0RiUgyqfARkYy2t2wvANnbCunVC3Jy0hyQiCSVCh8RyWhflH9Bbk4u2/7RU+N7RDKACh8RyXh9O/dl2btZGt8jkgFU+IhIxuvXuR9LlmhGl0gmCLzwMbP2ZvaMme01s1VmdkEtx5mZ3W1mW2Nf95iZBR2PiERbKnLKqUf3Y9ky6N072NhFJHySsXLzg0AZkA/0AV40s6XOueU1jpsCjAeKAAe8DHwE/DoJMYlIdCU9p3Qs60deHrRtG2jcIhJCgbb4mFkuMAG4yTm3xzn3BvA8cFGcwy8B/ss5t9Y59ynwX8DkIOMRkWhLRU7p0aEH2z/sSd++AQYuIqEVdItPT6DcOVda7b6lwNA4xxbGHqt+XGG8JzWzKfhPcwD7zey9AGJNho7AlnQHUYcwxxfm2CDc8YU5NoDGrIyTkpwy6cLs9/z9jYg0OcL+tw1zfGGODcIdX5hjg8bllMALn1bAzhr37QRa1+PYnUArMzPnnKt+oHNuBjADwMwWOuf6BxdycMIcG4Q7vjDHBuGOL8yxgY+vET+unBLS2CDc8YU5Ngh3fGGODRqdUwIf3LwHaFPjvjbA7noc2wbYUzNBiUhGU04RkUAFXfiUAtlm1qPafUVAzUGIxO4rqsdxIpK5lFNEJFCBFj7Oub3A08BtZpZrZoOBccDjcQ5/DPihmR1rZscAU4GZ9TjNjKDiTYIwxwbhji/MsUG44wtzbNCI+JRTQh0bhDu+MMcG4Y4vzLFBI+OzoFuBzaw98CgwCtgKXO+ce8LMhgD/55xrFTvOgLuBy2M/+jBwnZqlRaQ65RQRCVLghY+IiIhIWGnLChEREckYKnxEREQkY4Su8An7Xl8NiO8WM/vCzPZU++qW5NiuMrOFZrbfzGYe5thrzWyDme00s0fNrHkYYjOzyWZWXuO6DUtybM3N7JHY33O3mS02szPrOD5l164hsaXj2sXOO8vM1pvZLjMrNbPL6zg2pa+72DmVUxKPTTklsdhCm1MaGl+arl9yc4pzLlRfwGzgj/jFyL6OX4SsMM5x3wU+AI4DjgVWAFeEKL5bgFkpvnbn4PcqegiYWcdxo4GN+FVt2wHFwE9CEttk4I0UX7fc2N/rBPyHgW/i14k5Id3XroGxpfzaxc5bCDSPfV8AbAD6pfvaVTuvckrisSmnJBZbaHNKAvGl4/olNaek7BdpwB+jDOhZ7b7H4/0iwFvAlGq3vw3MC1F8KU9S1c59x2ESwRPAndVujwA2hCS2lL/JaonjXWBCmK5dPWJL+7XDLyW/Hjg3DNdOOSWwOJVTGh9naHPKYeJL6/VLRk4JW1dXbfvyxNtvp9778gSoIfEBnGVm28xsuZldmeTYGiLetcs3sw5piqemU81sS6yJ8yYzC3prlTqZWT7+bx1v8bu0XrvDxAZpunZm9isz+wz4Oz5J/W+cw9Jx7ZRTUkM5pQ5hzikQzrySzJwStsInkH15khRbvHNWnjdefE8CvYA84DvAj8zs/CTG1hDxrh3E/z1S7TXgq0An/K7c5wPTUnVyM8sBfg/8zjn39ziHpO3a1SO2tF0759z38NdgCH7Bwf1xDkvHtVNOSQ3llFqEOadAePNKMnNK2AqfsO/LU+/4nHMrnHPrnHPlzrm3gAeAbyUxtoaId+0g/nVOKefcR865j51zFc65ZcBtpOi6mVkzfDdDGXBVLYel5drV3Y7NvAAAA8RJREFUJ7Z0XrvY+cudc2/gx8jEa41Ix7VTTkkN5ZQ4wpxTIPx5JVk5JWyFT9j35WlIfDU5IOkzROop3rXb6JzbmqZ46pKS6xb7VP8IkI/v5/6ilkNTfu0aEFtN6XrNZQMnxbk/Ha875ZTUUE6pIcw5pYHx1ZSO112wOSVdA5bqGMj0B/wsh1xgMLXPcLgCeB8/++KY2AVIxQyM+sY3Dj/K3ICBwKfAJUmOLRtoAdyFr+JbANlxjhuDHyX/lViMr5L8WQT1je1MID/2fQHwHnBzCv6uvwbmAa0Oc1w6rl19Y0v5tcM3f0/ENzln4WdZ7AXGheHaxc6rnJJ4bMopiccX2pzSwPhSev1SkVOSemET/KXbA8/GftHVwAWx+4fgm50rjzPgHmBb7OseYltwhCS+2fh9hfbgB2ddnYLYbsFX49W/bgG6xuLoWu3YH+KnAe4Cfkts6mC6YwPujcW1F/gI36yak+TYjo/F83kslsqvC9N97RoSW5quXR7wN2BH7HosA74Teyztr7vYOZVTEo9NOSWx2EKbUxoaX6qvXypyivbqEhERkYwRtjE+IiIiIkmjwkdEREQyhgofERERyRgqfERERCRjqPARERGRjKHCR0RERDKGCh8RERHJGCp8REREJGOo8BEREZGMocJHUsLMWprZWjNbbWbNazz2sJmVm9nEdMUnItGinCKJUuEjKeGc2wfcDHQBvld5v5ndBXwb+L5z7g9pCk9EIkY5RRKlvbokZcwsC1iK3323G3A58DP8Tr+3pTM2EYke5RRJhAofSSkz+ybwP8ArwD8Dv3TOXZ3eqEQkqpRTpKHU1SUp5Zx7AXgHGAH8EfhBzWPM7N/MbL6ZfW5mxSkOUUQiRDlFGio73QFIZjGzc4E+sZu7Xfwmx/XAT4ABwKBUxSYi0aOcIg2lwkdSxszOAB4HngG+AC4zs585596vfpxz7unY8V1TH6WIRIVyiiRCXV2SEmZ2GvA08CZwITAdqADuSmdcIhJNyimSKBU+knRm1gt4ESgFxjvn9jvnVgKPAOPMbHBaAxSRSFFOkcZQ4SNJFWtafgnYCZzpnNtV7eHbgH3APemITUSiRzlFGktjfCSpnHOr8QuMxXtsPXBkaiMSkShTTpHGUuEjoWNm2fjXZjbQzMxaABXOubL0RiYiUaScItWp8JEwmo5fir7SPuBvwLC0RCMiUaecIgdp5WYRERHJGBrcLCIiIhlDhY+IiIhkDBU+IiIikjFU+IiIiEjGUOEjIiIiGUOFj4iIiGQMFT4iIiKSMf4fa8H1ZWM+ftEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: to be future-proof, we set `max_iter=1000` and `tol=1e-3` because these will be the default values in Scikit-Learn 0.21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.47012588])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", max_iter=1000, tol=1e-3, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ageron/miniconda3/envs/tf2/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:475: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 2.802867703827461, tolerance: 0.0009294783355207351\n",
      "  positive)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Early stopping example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from sklearn.base import clone\n",
    "\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler())\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(sgd_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239,\n",
       " SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "              eta0=0.0005, fit_intercept=True, l1_ratio=0.15,\n",
       "              learning_rate='constant', loss='squared_loss', max_iter=1,\n",
       "              n_iter_no_change=5, penalty=None, power_t=0.25, random_state=42,\n",
       "              shuffle=True, tol=-inf, validation_fraction=0.1, verbose=0,\n",
       "              warm_start=True))"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[1, 1], [1, -1], [1, 0.5]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 727.2x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.05, n_iterations = 200):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + l2 * theta\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 2., 0, \"Lasso\"), (1, N2, 0,  2., \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(np.array([[2.0], [0.5]]), Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, N / 2., levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", fontsize=16, rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title, fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename']"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris virginica, else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: To be future-proof we set `solver=\"lbfgs\"` since this will be the default value in Scikit-Learn 0.22."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='l2',\n",
       "                   random_state=42, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12718b5c0>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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B4HrgFg/Gq1Sx1a8PL71k1wcMgP37nY3Hm77d+i2v/vIqYSFhzLh5BpFhkU6HpHyAW/3ojTFHgJtdbP8Be7E27/lhbE8bpXxK377w6afwww/wyy9w001OR+R5iWmJ3D/vfgBGXj6SllVbOhyR8hU6Hr0KCiJ2Zqq0tMC9kWrwgsHsTNxJ62qtGdZxmNPhKB+iiV4FjUDuxbtkxxLe+u0tIkIjmH7zdMJC9L+2yqejGqmgY4wdEydQeuGkZ6XTd35fAIZ1GEaj+EYOR6R8jX7tq6Czezf072/Hrb/5Zrj6aqcjKpnxS8ez6fAm6leqz7AO2mSjTqc1ehV0atSAESPs+oABkJ7ubDwlsfHQRsYtHQfA1Bunai8b5ZImehWUHn8cGjSAzZvhhRecjubc5JgcHvr8ITKyM3ig5QN0qt3J6ZCUj9JEr4JSRARMnmzXx46FbducjedczFw1kyU7lnBezHlM7DLR6XCUD9NEr4LWlVdCjx62y+Ujj/jX9IPH04/z5MInAfhXl39RMbqiwxEpX6aJXgW1F16AuDhboz961Olo3Pfs4mfZn7KftjXacnezu50OR/k47XWjglrVqrBoETRtaptz/MGmQ5t4ZfkrCMK/r/u3zv2qiqSJXgW9Sy5xOgL3GWN47OvHyMzJ5IGWD5BQLcHpkJQf0KqAUrn277c3UfnyoGdf/PEFX235irjIOMZdNc7pcJSf0Bq9UrkeeQQ+/hgyM2HqVKejOV1GdgYDvx4IwOgrRnNezHkOR6T8hdbolco1ZgyEhdnBz1atcjqa001dOZUtR7bQoHIDBrQe4HQ4yo9oolcqV4MG0K+fnXpw0CDf6m6ZmJbImCVjAJhw9QTCQ8Mdjkj5E030ShXwzDNQoYLtifP5505Hk2/ijxM5dOIQHWt15KaLA3AwfeVVmuiVKqBSpfxxcJ56CrKznY0HYNfxXbz484uAvTlKRByOSPkbTfRKFdK/P1xwAaxdC0uWOB0NPPPdM6RlpXF7o9u5rMZlToej/JD2ulGqkMhIePNNKF8eWrd2NpY1+9cwfZWdSES7U6pzpYleKRe6dHE6Amvot0PJMTkMaD2Aiype5HQ4yk9p041SRfjhB0hMLP39Lt6+mC//+JKyEWUZcfmI0g9ABQxN9EqdxdNPw+WXl/6Y9cYYnv7uaQAGtxtMfEx86QagAoomeqXO4vrr7eOLL5bu0AgL/lzA0p1LqRRdicfaPFZ6O1YBSRO9UmfRrh107QonTsCECaWzT2MMI76zTTVPtn+SuMi40tmxClia6JUqwhh7QypTpsCePd7f3/zN81mxZwVVYqow4FId6kCVnCZ6pYrQvDl0725noho/3rv7yjE5J2vzT3V8ijLhZby7QxUUNNEr5YZRo0DEjmq5a5f39vPp+k9ZvX81NeJq0PeSvt7bkQoq2o9eKTc0aQL33muHSIiO9s4+snOyGfn9SACe7vg0UWFR3tmRCjqa6JVy09tv21q9t3yw5gM2HtpInfJ1uK/lfd7bkQo62nSjlJsKJnlPD2GcnZN9chjiZzo9Q0Son0xgq/yCW4leRCqKyBwRSRGRHSLS4yxlW4nIEhFJFpH9IvKo58JVynnvvQeNGsG2bZ77zI/WfcSWI1uoW6EuPZv19NwHK4X7NfrJQAZQBegJTBGRxoULiUhl4CtgKlAJuAhY4JlQlfINCxbAxo0wdqxnPi/H5DBuqR2wbGj7oYSFaIuq8qwiE72IxADdgRHGmGRjzFJgHtDLRfFBwNfGmPeNMenGmCRjzAbPhqyUs0aMgJAQmDEDtm8v+efN3zSftQfWUr1sde5pfk/JP1CpQtyp0V8MZBtjNhfYtgo4rUYPtAGOiMhPInJAROaLSC1XHyoifUVkpYisPHjwYPEjV8oh9epBjx6QlQUTJ5bss4wxPPfDcwAMaTeEyLBID0So1KncSfSxQOGx+xKBsi7K1gDuBR4FagHbgFmuPtQY84YxJsEYkxAfrwM2Kf8ybJi9ODttWsnulv1227es2LOC+DLx9Lmkj+cCVKoAdxJ9MlB4sI04IMlF2VRgjjFmhTEmDRgNtBORciULUynf0qiRvVs2I6NkI1vm1eYHthmod8Eqr3En0W8GwkSkXoFtzYF1LsquBgp2PMtb10kuVcAZPtw+fvmlbcYprp/++onvt39Puchy9G/d37PBKVVAkYneGJMCzAbGiEiMiLQHugEzXRR/B7hFRFqISDgwAlhqjDnmyaCV8gUtWsB//wurV0PYOXSUyavNP3LpI5SL0h+9ynvc7V7ZH4gGDmDb3PsZY9aJSEcRSc4rZIxZBDwFfJFb9iLgjH3ulfJ3f/sbRJzDvU2/7f2NL//4kjLhZXi0jd5qorzLrXqIMeYIcLOL7T9gL9YW3DYFmOKR6JTyE4cOwZo10Lmze+Xz+s0/dMlDVC5T2YuRKaVj3ShVYjt2QOPGtma/YweUddUfrYANBzfw6fpPiQiNYHC7waUTpApqOtaNUiV0wQXQqhUcPWonJynK+B/HYzDc1+I+qpWt5v0AVdDTRK+UBzxt5/Fm0iQ77eCZbD+2nfdXv0+ohPJk+ydLJzgV9DTRK+UBXbpA69Zw4AC88caZy038cSLZJpseTXtQp0Kd0gtQBTVN9Ep5gEh+rf6FFyA9/fQye5P28vZvbyMIwzoMK90AVVDTRK+Uh9x4IzRtCrt32wHPCpu0bBLp2enc2vBWGsY3LP0AVdDSRK+Uh4SE2DFwOneGhoXy+OETh3l95esADO843IHoVDDT7pVKedCdd8Jdd52+/ZXlr5CSmcJ1F11Hy6otSz8wFdS0Rq+UB7maU/Z4+nFe/eVVAJ7q+FQpR6SUJnqlvGL1arj9dvjsM3htxWscSzvG5RdcTodaHZwOTQUhbbpRygsWL4ZPPoE/t2bz199fBLRtXjlHa/RKecGDD8J558Fv/wvl0JoWJFRLoEvdLk6HpYKUJnqlvCA6Gh59LHeQ+h+GM7zjcMRVA75SpUATvVJeEtf+A4g6Cjs6UfFgV6fDUUFME71SXpCVk8Urq56Fy/4NwPPj9L+aco7+61PKCz5e9zFbjmyh9rXziYkxLFwIO3c6HZUKVtrrRikPyzE5JycWGX7tP6jUQGjZEmrVcjgwFbQ00SvlYfM3zWftgbVUL1udXs16EdnK6YhUsNOmG6U8yBhzctLvIe2GEBkWefK1nBz49VenIlPBTBO9Uh60cOtCVuxZQXyZePpc0ufk9sxMSEiAyy6DrVsdDFAFJU30SnlQXtv8wDYDKRNe5uT28HBo1gyys2HCBKeiU8FKE71SHvLTXz/x/fbvKRdZjv6t+5/2+rBhdtCz6dPtmPVKlRZN9Ep5yNglYwF45NJHKBdV7rTX69eH226DjAw7C5VSpUUTvVIe8OueX/nvlv8SEx7Do20ePWO5p3JHKZ46FQ4eLKXgVNDTRK+UB+T1tOmX0I/KZSqfsVyLFnD99ZCaCi+/XFrRqWCniV6pElp7YC1zNs4hKiyKx9s9XmT54cOhShWoVq0UglMKvWFKqRLLq833adWH82PPL7J8u3awYwdERhZZVCmP0Bq9UiWw6dAm/rP2P4SHhDOk3RC336dJXpUmTfRKlcD4H8djMPRu0Zua5WoW672JifD88/D2214KTqlcbiV6EakoInNEJEVEdohIjyLKR4jIRhHZ5ZkwlfI9249tZ+aqmYRKKEM7DC32+5cssb1wRoyA9HQvBKhULndr9JOBDKAK0BOYIiKNz1J+CHCghLEp5dMmLJ1AtsmmR9Me1K1Qt9jvv+EGaNoU9uyBd9/1QoBK5Soy0YtIDNAdGGGMSTbGLAXmAb3OUL4OcDfwvCcDVcqX7D6+m7d/fxtBGNZh2Dl9RkhIfr/6CRMgK8uDASpVgDs1+ouBbGPM5gLbVgFnqtG/CjwFpJYwNqV81gs/vUBGdga3NbqNhvENz/lzbr8d6tWzA5395z8eDFCpAtxJ9LFAYqFtiUDZwgVF5BYgzBgzp6gPFZG+IrJSRFYe1FsElR/Zn7yfqb9OBWB4x+El+qzQUBia27w/bpwdylgpT3Mn0ScDcYW2xQFJBTfkNvFMBB5xZ8fGmDeMMQnGmIT4+Hh33qKUT5j440RSs1LpWr8rzc9vXuLPu/tuqFkT1q+HBQs8EKBShbhzw9RmIExE6hlj/sjd1hxYV6hcPaA28IOIAEQA5URkH9DGGLPdIxEr5aC9SXt5beVrAIzqNMojnxkRYYdDiIiAa6/1yEcqdYoiE70xJkVEZgNjRORBoAXQDWhXqOhaoGBH4nbA/wGtAG2bUQFh/NLxpGWlcUuDW2hZtaXHPvfWWz32UUqdxt3ulf2BaGyXyVlAP2PMOhHpKCLJAMaYLGPMvrwFOALk5D7P9kr0SpWi3cd3n2ybH3XFKK/tZ+tWMMZrH6+CkFuJ3hhzxBhzszEmxhhTyxjzQe72H4wxsWd4z/fGmBqeDFYpJz2/9HnSs9O5vdHtNKvSzCv7GDrU9sKZU2R3BqXcp0MgKOWGvxL/4s3/vYkgPNPpGa/tp2ZN2/Nm5Eg77aBSnqCJXik3jPthHBnZGfy9yd9pfN7ZbgovmQcfhFq1YN06+Ogjr+1GBRlN9EoVYfux7Uz7bRohEuLV2jzYUS1HjrTrzzyjd8sqz9BEr1QRxi4ZS2ZOJj2a9qBB5QZe398998CFF8Iff8B773l9dyoIaKJX6iw2HtrIO7+/Q6iEMvLykaWyz/BwGDXKro8ebScTV6okNNErdRbDFw0nx+TwYKsHqVepXqnt9667oHFjaNsWkpKKLq/U2ehUgkqdwfJdy5m9YTbRYdGM7FQ6tfk8oaGwYgVER5fqblWA0hq9Ui4YY3hy4ZMAPHrZo1QrW/ozeWuSV56iiV4pF77a8hWLdyymQlQFnuzwpKOxLFoEV1wBB3QqH3WONNErVUiOyWHYt3YykWEdhlE+qryj8bz4IixeDGPGOBqG8mOa6JUqZNaaWazav4oacTV4+NKHnQ6H8ePtbFRTp8LmzUWXV6owTfRKFZCamcpTi+z8fqM6jSI63PmG8iZN4L777M1TeVMPKlUcmuiVKuCln19iZ+JOmlVpRu8WvZ0O56TRo+3F2U8/hWXLnI5G+RtN9Erl2pu0l3E/jAPgpWtfIjQk1OGI8lWvDoMG2fXBg3UYY1U8muiVyvX0oqdJyUyha/2uXFnnSqfDOc0TT0B8PGzcaMesV8pdesOUUsD/9v6Pd35/h/CQcF7o8oLT4bgUF2fHqW/YECpWdDoa5U800augZ4xh0NeDMBgeufSRUh3qoLjat3c6AuWPtOlGBb1PN3zK4h2LqRRdiRGdRjgdjlvS0my3S23CUe7QRK+CWlJ6Eo999RgAY68c6/jNUe4aPhyGDYPHH3c6EuUPNNGroDZ68Wh2J+2mdbXW9GnVx+lw3Pb44xATA3PnwoIFTkejfJ0mehW01uxfw8s/v4wgTLlhik91pyxKtWowIreV6eGHbVOOUmeiiV4FpRyTQ78v+pFtsunfuj+XVLvE6ZCKbeBA2wPnjz9g3Dino1G+TBO9CkozVs3gx79+5LyY8xh75VinwzknERHwxht2ffx4WL/e2XiU79JEr4LOwZSDDPlmCACTrpnkNxdgXenQAfr2hcxMmD7d6WiUr9J+9Cro/POrf3LoxCE61+5Mz6Y9nQ6nxMaPh06d7PSDSrmiiV4Flbkb5/Lh2g8pE16Gt7q+hYg4HVKJVagAPXo4HYXyZdp0o4LG0dSj9PuiHwDPX/U8dSvUdTgiz9u82Q5lrIOeqYK0Rq+CxqAFg9iXvI/2Ndv7xIQinpaebqcc3LsX6tWzY9grBVqjV0Hii81fMP336USGRjKt6zRCJPD+6UdGwoQJdv3RR2HHDmfjUb4j8P61K1XI/uT93D/vfsAOc1C/cn2HI/Keu++Gm2+GpCS4/37IyXE6IuUL3Er0IlJRROaISIqI7BARl5d+RGSIiKwVkSQR2SYiQzwbrlLFY4zh/nn3cyDlAFfWuZJBbQc5HZJXidi5ZStXhkWLYPJkpyNSvsDdGv1kIAOoAvQEpohIYxflBLgHqAD8DXhYRO70RKBKnYvXVrzGl398SYWoCrx787sB2WRT2Hnn2WQPdjaq3393Nh7lvCIg+SCDAAARm0lEQVT/1YtIDNAdGGGMSTbGLAXmAb0KlzXGTDTG/M8Yk2WM2QR8BugI2soR6w6sY/A3gwF486Y3qRFXw+GISs+tt9obqUTsjFQquLlTvbkYyDbGbC6wbRXgqkZ/ktgOyh2BdWd4va+IrBSRlQcPHnQ3XqXckpKRwt8/+TtpWWnc3+J+ujfq7nRIpe7ll2HlSrhTf1MHPXcSfSyQWGhbIlC2iPeNyv38d1y9aIx5wxiTYIxJiI+PdyMMpdxjjKHP/D6sO7iOBpUb8Mp1rzgdkiOio6FJk/znqanOxaKc5U6iTwbiCm2LA5LO9AYReRjbVn+DMSb93MNTqvheW/Eas9bOIiY8htl3zCY2ItbpkBz33ntQpw6sWuV0JMoJ7iT6zUCYiBScSLM5Z26SuR8YClxljNlV8hCVct/Pu35m4NcDAZjWdRoN4xs6HJFvWLgQ9u+Hbt3g0CGno1GlrchEb4xJAWYDY0QkRkTaA92AmYXLikhPYBzQxRijs1mqUrU3aS+3f3w7mTmZPHrZo/y9yd+dDslnvP46tG5tb6K64w472qUKHu72NesPRAMHgFlAP2PMOhHpKCLJBcqNBSoBK0QkOXd53bMhK3W6E5kn6PZhN3Yd30X7mu2Z2GWi0yH5lKgomD0bqlSB776z3S5V8HBrrBtjzBHgZhfbf8BerM17XsdzoSnlnhyTw71z72XFnhXUKV+HOX+fQ0RohNNh+ZwaNWyyv+IK+Pe/oVEjeOghp6NSpSHw7x5RAW/kdyP5ZP0nxEXG8XmPz4mP0V5cZ9KuHUyZYteHDoUjR5yNR5UOHb1S+bUpK6bw3A/PESqhfHTbRzSKb+R0SD7vgQfg2DG48kqoWNHpaFRp0ESv/NasNbMY8OUAAKbcMIVrL7rW4Yj8x+OPn/o8I8POQasCkzbdKL/03z/+yz1z78FgeP6q5+lzSR+nQ/JbM2fa9vpt25yORHmLJnrldxZtW0T3j7qTlZPF4LaDebL9k06H5LeysuwAaH/+aZtydu50OiLlDZrolV/55s9vuOGDG0jNSuXBlg8yscvEgJj31SlhYfDll3DZZbB9O3TuDLv0NseAo4le+Y2vt3zNTbNuIi0rjT6t+jD1pqma5D0gLg6++goSEmDrVpvst293OirlSZrolV/4ZP0ndPuwG+nZ6fRL6MfrN74eFGPLl5by5WHBAmjVCrZssd0w16xxOirlKfo/Rfm8V5e/yh0f30F6djr/vPSfTL5+siZ5L6hQwc5K1amTHelSfywFDu1eqXxWjsnhqW+fYsKPdsbrcVeOY2iHodpc40XlytlmnD/+OHWIY+XfNNErn3Q8/Tj3zLmHzzZ9RqiEMq3rNO5tca/TYQWFqCho2jT/+f/9Hxw+DCNGQIj+kPJLmuiVz/nj8B90+7AbGw5toHxUeT7s/qHeDOWQXbvszVUZGbB2LUyfDjExTkeliku/n5VPmbdpHq3fbM2GQxtoFN+IXx78RZO8g2rUgDlzbM+cTz6BNm1gncuZKJQv00SvfEJqZioDvhhAtw+7kZieyM0NbubnB36mXqV6Rb9ZedX118Py5VC/vq3Vt24Nb74JxjgdmXKXJnrluNX7V9P6zda8tvI1wkPCmXTNJD6941PKRhY1LbEqLQ0a2InGe/e2PXL69oUJE5yOSrlLE71yTHpWOiO/G0nCGwmsO7iO+pXqs/zB5QxqO0i7T/qg2Fh45x07/2y1atCjh9MRKXfp/ybliKU7l9JiagueXfIsmTmZ/OOSf/Br319pWbWl06GpIvTsacfGqVXLPs/JgeHDdZwcX6aJXpWqnYk76Tm7Jx3f6cjGQxtpULkBS3ovYcqNU4iJ0O4c/iIqKn/99ddh3Djbhj9yJKSkOBeXck0TvSoVSelJDP92OPX/rz4frPmAyNBIRl4+kt8f+p2OF3R0OjxVAt26wV13QVoaPPusTfgzZkB2ttORqTya6JVXJaUnMX7peOr+uy7jlo4jLSuNO5vcycaHNzK682giwyKdDlGVUPXq8MEHsHQpXHIJ7N4N995r76ydP9/p6BToDVPKS46kHmHyL5N56eeXOJp2FIB2NdvxQpcXaFuzrcPRKW9o3x5++cVOZDJqFGzcaJO+cp4meuVRq/ev5tXlr/L+mvdJzUoFoEOtDjzT6RmuqnOVjlMT4EJCbG2+Rw+YNQvuvDP/teeesxOd/OMfUKWKczEGIzE+cNdDQkKCWblypdNhqHOUnJHMnA1zeOu3t1iyY8nJ7ddceA3DOgyj0wWdNMEHuaQke5ft8eN2btru3e0XwtVXQ2io09H5LxH51RiTUFQ5rdGrc5Kdk823275l5uqZzN4wmxOZJwCIjYild/PePHzpw9SvXN/hKJWviI2FuXPhlVdg3jxb2581y7bv3303PPKIXVfeoTV65bbkjGQW/LmAeZvm8fnmzzmcevjka+1qtqNXs170aNqDuMg4B6NUvm7HDtsr5913bX98sJOc5A2LvHevbdrRkTKL5m6NXhO9OqMck8Oqfav4bvt3LNy6kEXbFpGenX7y9XoV69GzaU/ubnY3F1a80MFIlT8yBn780c5Z+9xz+ROdXHopbNsGV11lm3auvhpq13Y0VJ+liV4VW2pmKr/t+41fdv/C99u/Z8mOJSd7zAAIQpsabehavytd63elYeWG2vauPCo5GZo1s4m+oAsvhA4d7IXcNm2cic0XaRu9OqtjacdYf3A9a/avYeWelazYs4K1B9aSbU69y6V2+dp0rt2ZK2pfwbUXXkuVWO0uobwnNtY252zeDAsX2mXRIrvtzz+ha9f8snPnwpIl9ouhWTNo1OjUO3ZVPk30ASwtK40dx3aw/dh2th7dysZDG1l/aD3rDqxjb/Le08qHSAjNqjQjoWoCHWp1oHOdztQuX7v0A1dBTcTeXVu/PgwYYLtk/vYbLFsGHQvcRD1vnh1kLU9oKNSrZxN+27YweHD+a8YE9xy4biV6EakITAOuAQ4Bw4wxH7goJ8B44MHcTdOAJ40vtA8FmKT0JPYl7zu57E3ey77kffx1/C+2Hd3GtmPb2JO054zvjw6LpmF8QxrHN6ZV1Va0rtaallVbUia8TCkehVJFCwuzY+C3bn3q9vvus006q1fbZfNme5PWxo22CSgv0Scl2Yu7F1xge/bUqGGXvPW2baFy5dI/rtLkbo1+MpABVAFaAF+IyCpjTOG5ZvoCNwPNAQN8A2wFXvdMuIHBGENGdgYpmSmkZKSQkplCckYySelJHE07ytHUo6c8Hkk9cvL54dTD7E/eT0pm0SNHhUooNcvVpE75OtQpX4f6levTKL4RjeIbUbt8bR0KWPm1jh1PreGnpsKGDbBpE5Qvn7992zb7Wt6XQGFffw3XXGPXx461vxLi423yz1sqVICaNeGee/Lf99tvdlrFuDi7REf77q+GIhO9iMQA3YEmxphkYKmIzAN6AUMLFb8XmGSM2ZX73klAH7yU6JMzkknJSCHbZJOdk02OyTm5nm1yn+euF2dbwc/JyskiIzuDjOwM0rPT89ez0l1vL1TmROaJ0xJ6XswlERUWRdXYqpwfez5Vy1bl/JjzOT/2fKrHVbeJvUIdasTVICxEW+dUcIiOhlat7FJQs2aQmGiHUd69286Du2tX/nrduvlld+6ErVvtUlizZvmJ3hjbOygrK//10FAbQ3Q0/Otf9oYwgC++gEmT8l/LW6Ki7L4fe8yzfwdX3MkCFwPZxpjNBbatAjq5KNs497WC5Rqfe3hnN2TBEF7/1T9/LISHhBMTEUNMeAwxETHERsQSGxFLhagKVIiuYB8LrkdXoGJ0RSpEVeD82POJi4zTHi9KuSkuzvbTz+urfyYvvGCbfA4dyl8OHoRjx05t3snMhObN7RfI8eN2SUuzTUbJyad+AezYAd9953p/l13mO4k+FkgstC0RcDXPW+GyiUCsiEjhdnoR6Ytt6qFW3gwGxVQuqhzxZeIJDQklVEIJkZCT68XZFiIhp7xecFtYSBiRYZFEhEQQERph10Nz10Mjz7gtbykTXuZkIs9L6jHhMYSHhp/TMSulvCevGebii89eLiLCTq1YUFaWbSJKTbVNOnm6dbMXlvNeK7icd57nj8GVIvvRi0hL4EdjTJkC2x4HrjDG3FSobCLQxRjzS+7zS4DvjTFnnfxT+9ErpVTxuduP3p2rcZuBMBGpV2Bbc6DwhVhytzV3o5xSSqlSUmSiN8akALOBMSISIyLtgW7ATBfFZwCDRKS6iFQDHgemezBepZRSxeRu/7r+QDRwAJgF9DPGrBORjiKSXKDcVGA+sAZYC3yRu00ppZRD3Op7Z4w5gu0fX3j7D9gLsHnPDfBE7qKUUsoH6B0zSikV4DTRK6VUgNNEr5RSAU4TvVJKBTifmHhERA4CO87x7ZWxI2oGAj0W3xQoxxIoxwF6LHkuMMbEF1XIJxJ9SYjISnfuDPMHeiy+KVCOJVCOA/RYikubbpRSKsBpoldKqQAXCIn+DacD8CA9Ft8UKMcSKMcBeizF4vdt9Eoppc4uEGr0SimlzkITvVJKBTi/SPQiUlFE5ohIiojsEJEeZygnIjJBRA7nLhPFx+bbK8axjBKRTBFJLrDUdVXWCSLysIisFJF0EZleRNmBIrJPRBJF5G0RiSylMIvk7nGISG8RyS50Pq4ovUiLJiKRIjIt999Vkoj8JiLXnaW8T56X4hyHn5yX90Rkr4gcF5HNIvLgWcp65Zz4RaIHJgMZQBWgJzBFRFzNRdsXO8pmc6AZcCPwUGkF6SZ3jwXgP8aY2AKLiymLHbMHGAu8fbZCInItdhL5q4DaQF1gtLeDKwa3jiPXskLn43vvhlZsYcBf2PmcywEjgI9EpHbhgj5+Xtw+jly+fl6eB2obY+KArsDY3Nn3TuHNc+LziV5EYoDuwAhjTLIxZikwD+jlovi9wCRjzC5jzG5gEtC71IItQjGPxacZY2YbY+YCh4soei8wzRizzhhzFHgWHzonxTgOn2eMSTHGjDLGbDfG5BhjPge2AaclFXz4vBTzOHxe7t84Pe9p7nKhi6JeOyc+n+iBi4FsY8zmAttWAa5qwY1zXyuqnFOKcywAN4nIERFZJyL9vB+eV7g6J1VEpJJD8ZRESxE5lPvze4SIuDWfg1NEpAr235yr6Tz95rwUcRzgB+dFRF4TkRPARmAv8KWLYl47J/6Q6GOBxELbEgFXE44XLpsIxPpQO31xjuUjoCEQD/QBRorIXd4NzytcnRNwfcy+bAnQBDgP+6vsLmCIoxGdhYiEA+8D7xpjNroo4hfnxY3j8IvzYozpj/3bdsROzZruopjXzok/JPpkIK7QtjggyY2ycUCy8Z2bBdw+FmPMemPMHmNMtjHmJ+AV4LZSiNHTXJ0TcH3+fJYxZqsxZltuU8IaYAw+ej5EJAQ7p3MG8PAZivn8eXHnOPzpvOT+X14K1ABc/UL32jnxh0S/GQgTkXoFtjXH9c+4dbmvFVXOKcU5lsIM4Cu/TIrD1TnZb4zx9zZxnzwfub9ep2Ev9nc3xmSeoahPn5diHEdhPnleCgnDdRu9186Jzyd6Y0wK9qfOGBGJEZH2QDfsN31hM4BBIlJdRKoBjwPTSy3YIhTnWESkm4hUyO0yeinwT+Cz0o34zEQkTESigFAgVESiztA2OgN4QEQaiUgF4Gl86Jy4exwicl1uWzEi0gDbE8RnzkcBU7BNfjcZY1LPUs6nzwtuHoevnxcROU9E7hSRWBEJze1ZcxewyEVx750TY4zPL0BFYC6QAuwEeuRu74htmskrJ8BE4EjuMpHcYR58ZSnGsczC9gRJxl7A+afTsRc6jlHk9yDIW0YBtXJjrlWg7CBgP3AceAeIdDr+4h4H8ELuMaQAW7FNBOFOx1/oWC7IjT8tN/a8pac/nZfiHIevnxfsNbbFwLHcv/MaoE/ua6V2TnSsG6WUCnA+33SjlFKqZDTRK6VUgNNEr5RSAU4TvVJKBThN9EopFeA00SulVIDTRK+UUgFOE71SSgU4TfRKKRXg/h+ig03FNzpSbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.66066066])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='multinomial', n_jobs=None, penalty='l2',\n",
       "                   random_state=42, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    n_classes = y.max() + 1\n",
    "    m = len(y)\n",
    "    Y_one_hot = np.zeros((m, n_classes))\n",
    "    Y_one_hot[np.arange(m), y] = 1\n",
    "    return Y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = np.sum(exps, axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.446205811872683\n",
      "500 0.8350062641405651\n",
      "1000 0.6878801447192402\n",
      "1500 0.6012379137693313\n",
      "2000 0.5444496861981873\n",
      "2500 0.5038530181431525\n",
      "3000 0.4729228972192248\n",
      "3500 0.4482424418895776\n",
      "4000 0.4278651093928793\n",
      "4500 0.41060071429187134\n",
      "5000 0.3956780375390374\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.32094157, -0.6501102 , -2.99979416],\n",
       "       [-1.1718465 ,  0.11706172,  0.10507543],\n",
       "       [-0.70224261, -0.09527802,  1.4786383 ]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6.629842469083912\n",
      "500 0.5339667976629505\n",
      "1000 0.503640075014894\n",
      "1500 0.49468910594603216\n",
      "2000 0.4912968418075477\n",
      "2500 0.489899247009333\n",
      "3000 0.48929905984511984\n",
      "3500 0.48903512443978603\n",
      "4000 0.4889173621830818\n",
      "4500 0.4888643337449303\n",
      "5000 0.4888403120738818\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.7096017363419875\n",
      "500 0.5739711987633519\n",
      "1000 0.5435638529109127\n",
      "1500 0.5355752782580262\n",
      "2000 0.5331959249285544\n",
      "2500 0.5325946767399383\n",
      "2765 0.5325460966791898\n",
      "2766 0.5325460971327977 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 \n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients\n",
    "\n",
    "    logits = X_valid.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    if loss < best_loss:\n",
    "        best_loss = loss\n",
    "    else:\n",
    "        print(iteration - 1, best_loss)\n",
    "        print(iteration, loss, \"early stopping!\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n",
    "\n",
    "logits = X_new_with_bias.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_test.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_test)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
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  "nav_menu": {},
  "toc": {
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